Complex flow patterns

Improvements ia membrane technology, vahdation of membrane iategrity, and methods to extend filter usage should further improve the performance of membrane filters ia removal of viral particles. Methods to improve or extead filter life and iacrease flow rates by creating more complex flow patterns could possibly be the focus of the next generation of membrane filters designed to remove viral particles. 

As discussed in Section 9.4.4, the complex flow pattern on the shell-side and the great number of variables involved make the prediction of coefficients and pressure drop very difficult, especially if leakage and bypass streams are taken into account. Until about 1960. empirical methods were used to account for the difference in the performance... 

The complex flow pattern on the shell-side, and the great number of variables involved, make it difficult to predict the shell-side coefficient and pressure drop with complete assurance. In methods used for the design of exchangers prior to about 1960 no attempt was made to account for the leakage and bypass streams. Correlations were based on the total stream flow, and empirical methods were used to account for the performance of real exchangers compared with that for cross flow over ideal tube banks. Typical of these bulk-flow methods are those of Kern (1950) and Donohue (1955). Reliable predictions can only be achieved by comprehensive analysis of the contribution to heat transfer and pressure drop made by the individual streams shown in Figure 12.26. Tinker (1951, 1958) published the first detailed stream-analysis method for predicting shell-side heat-transfer coefficients and pressure drop, and the methods subsequently developed... 

After introducing some types of moving-particle reactors, their advantages and disadvantages, and examples of reactions conducted in them, we consider particular design features. These relate to fluid-particle interactions (extension of the treatment in Chapter 21) and to the complex flow pattern of fluid and solid particles. The latter requires development of a hydrodynamic model as a precursor to a reactor model. We describe these in detail only for particular types of fluidized-bed reactors. 

Because of the complex flow pattern, it is not generally possible to determine visually the velocity at which the system ceases, in effect, to be a fluidised bed. From measurements of pressure fluctuations, the following approximate relation may be used, although with considerable care ... 

Thus far we have considered only two flow patterns the completely mixed reactor and the completely unmixed reactor. This is because only for these flow patterns can we completely ignore the fluid flow configurations in the reactor. In this chapter we will begin to see how reactors that have more complex flow patterns should be treated. We will not attempt to describe the fluid mechanics completely. Rather, we will hint at how one would go about solving more realistic chemical reactor problems and examine the errors we have been making by using the completely mixed and unmixed approximations. 

For any more complex flow pattern we must solve the fluid mechanics to describe the fluid flow in each phase, along with the mass balances. The cases where we can still attempt to find descriptions are the nonideal reactor models considered previously in Chapter 8, where laminar flow, a series of CSTRs, a recycle TR, and dispersion in a TR allow us to modify the ideal mass-balance equations. 

Even for systems with highly complex fluid dynamics, where the flow cannot adequately be approximated by a single chemical reactor, a network of ideal reactors may form the basis of a useful approximation. Because of the computational difficulties of handling mixing and chemical reaction in the complex flow patterns encountered in industrial applications,... 

A mixing time of only 2.9 s was derived [29], More complex flow patterns were determined than for all the arrays investigated so far. 

The virtual wall created can also be employed to carry out gas-liquid reactions. For instance, acetic acid vapor was allowed to react with a pH indicator solution at the virtual wall, allowing kinetic studies to be carried out (see Figure 3.21) [433], Moreover, using photocleavable SAM (with the 2-nitrobenzyl photosensitive group), the SAM can be patterned through a UV photomask, giving rise to complex flow patterns [433,434],... 

However, there exists a way to employ the rigorous equations of continuum mechanics even for the cases, in which real phase boundaries cannot be exactly localized. This way is associated with the idea of hydrodynamic analogy between complex and simpler flow phenomena. More precisely, some particular similarities are meant between complex flow patterns encountered in industrial separations and geometrically simpler flows like planar films, cylindrical jets, spherical drops, etc., as well as their combinations (Kenig, 1997). These similarities are used in the hydrodynamic analogy approach by which the complex hydrodynamics established in a real column is replaced with an appropriate combination of simpler flow patterns. Such a replacement occurs on the basis of experimental observations which are very important for the successful... 

Cross-flow over a cylinder exhibits complex flow patterns, as shown in Fig. 7-16, The fluid approaching the cylinder branches out and encircles the cylinder, forming a boundary layer that wraps around the cylinder. The fluid particles on Ihe inidplane strike Ihe cylinder at Ihe stagnation point, bringing the fluid to a complete stop and ihus raising the pressure at that point. The pressure decreases in the flow direction while the fluid velocity increases. 

Mass-Transfer Models Because the mass-transfer coefficient and interfacial area for mass transfer of solute are complex functions of fluid properties and the operational and geometric variables of a stirred-tank extractor or mixer, the approach to design normally involves scale-up of miniplant data. The mass-transfer coefficient and interfacial area are influenced by numerous factors that are difficult to precisely quantify. These include drop coalescence and breakage rates as well as complex flow patterns that exist within the vessel (a function of impeller type, vessel geometry, and power input). Nevertheless, it is instructive to review available mass-transfer coefficient and interfacial area models for the insights they can offer. 

---